Question

Given the data $$ \begin{array}{rr} \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}(g) & \Delta H=+180.7 \mathrm{~kJ} \\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) & \Delta H=-113.1 \mathrm{~kJ} \\ 2 \mathrm{~N}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g) & \Delta H=-163.2 \mathrm{~kJ} \end{array} $$ use Hess's law to calculate \(\Delta H\) for the reaction $$ \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{NO}_{2}(g) \longrightarrow 3 \mathrm{NO}(g) $$

Short answer

The enthalpy change for the target reaction \(N_2O(g) + NO_2(g) \longrightarrow 3NO(g)\) is \(\Delta H = +194.7\, kJ\).

Step-by-step solution

Write down the given data

The following three reactions and their enthalpy changes are given: 1. \(N_2(g) + O_2(g) \longrightarrow 2NO(g)\); \(\Delta H = +180.7\, kJ\) 2. \(2NO(g) + O_2(g) \longrightarrow 2NO_2(g)\); \(\Delta H = -113.1\, kJ\) 3. \(2N_2O(g) \longrightarrow 2N_2(g) + O_2(g)\); \(\Delta H = -163.2\, kJ\)

Determine the target reaction

The target reaction we want to calculate the enthalpy change for is: \( N_2O(g) + NO_2(g) \longrightarrow 3NO(g) \)

Rearrange and/or manipulate the given reactions

We need to rearrange or manipulate the given equations so that they can be added up, resulting in the desired equation. Let's consider the following changes: - Reverse reaction 3 and divide it by 2: \(N_2(g) + \frac{1}{2}O_2(g) \longrightarrow N_2O(g)\); \(\Delta H = +81.6\, kJ\) - Reverse reaction 2: \(2NO_2(g) \longrightarrow 2NO(g) + O_2(g)\); \(\Delta H = +113.1\, kJ\)

Add the manipulated reactions

Add the manipulated reactions to obtain the target reaction: \[N_2(g) + \frac{1}{2}O_2(g) \longrightarrow N_2O(g)\] \[2NO_2(g) \longrightarrow 2NO(g) + O_2(g)\] \[N_2O(g) + NO_2(g) \longrightarrow 3NO(g)\]

Calculate the enthalpy change for the target reaction

Add the enthalpy changes of the manipulated reactions to get the enthalpy change for the target reaction: \(\Delta H_{target} = \Delta H_{modified\,3} + \Delta H_{modified\,2}\) \(\Delta H_{target} = +81.6\, kJ + 113.1\, kJ\) \(\Delta H_{target} = +194.7\, kJ\) The enthalpy change for the target reaction is \(\Delta H = +194.7\, kJ\).

Key concepts

Enthalpy Change

Enthalpy change is a measure of the heat content of a chemical system and represents the amount of thermal energy exchanged during a reaction at constant pressure. It is denoted by the symbol \( \Delta H \) and commonly expressed in units of kilojoules per mole (kJ/mol). Positive \( \Delta H \) values indicate endothermic reactions, which absorb heat from the surroundings. Conversely, negative \( \Delta H \) values signify exothermic reactions, which release heat.

Understanding enthalpy change is crucial as it helps predict whether a reaction is likely to occur spontaneously and assists in determining the stability of the reactants and products. In the exercise provided, we were presented with multiple reactions each with a specified \( \Delta H \) value.

Through the correct manipulation of these reactions under Hess's law, we can predict the enthalpy change for a new reaction. This principle allows students to effectively study not just the energy changes within individual reactions, but also the sum of reactions as part of a larger chemical process.

Chemical Reactions

Chemical reactions involve the breaking and forming of bonds between atoms, which leads to the transformation of substances. The law of conservation of mass states that matter is neither created nor destroyed in a chemical reaction, which means we must account for all reactants and products in a balanced chemical equation.

There are various reaction types, such as synthesis, decomposition, single replacement, and double replacement reactions. In thermochemistry, we pay close attention to the thermal energy changes associated with these reactions.

In demonstrating Hess's law, correct manipulation of the given chemical equations to reach the desired equation is essential. Each step in our provided solution carefully rearranged the initial reactions — expressing complex scenarios in simpler, stepwise reactions — to derive the target equation. This simplification is key to enhancing students' grasp of chemical reactions in relation to energy changes.

Thermochemistry

Thermochemistry is a branch of chemistry focused on the study of energy and heat associated with chemical reactions and phase changes. It is governed by the first law of thermodynamics, which ensures energy conservation, often analyzed through enthalpy changes in chemical processes.

The principle of Hess's law falls within thermochemistry and asserts that the total \( \Delta H \) for a chemical reaction is the same, regardless of the number of steps taken to obtain the reaction. Hence, thermochemistry provides the tools to not only quantify energy changes but also to understand the pathway-dependent and pathway-independent nature of energy transformations.

The exercise we tackled is a direct application of thermochemistry. By carefully following Hess's law, we can determine the enthalpy change of a reaction even without performing the reaction in a lab. This theoretical approach saves time and resources, proving thermochemistry's critical role in both education and industry.